Transformed Schatten-1 penalty based full-rank latent label learning for incomplete multi-label classification

Incomplete multi-label learning is a challenging issue due to the difficulty of revealing low-rank structure of multi-labels. There is already much literature to tackle the challenge by imposing penalties of nuclear norm and matrix factorization. However, nuclear norm based methods treat all singular equally and deviate significantly from the approximation of rank of a matrix, whereas matrix factorization technique ignored class structure of latent labels. To address the two issues, in this paper, a transformed Schatten-1 penalty based full-rank latent label learning (TS1FRLL) method is proposed for incomplete multi-label classification. In this model, an improved transformed Schatten-1 regularization is proposed to approximate rank function in the circumstance of labels missing. To preserve the consistency of class structure of latent labels with that of original labels, both low-rank and row full-rank constraints are imposed on the multi-label matrix factorization. The c-block segmentation constraint and manifold learning are combined to characterize the global and local topological structure of latent labels. A classifier is collaboratively learnt to predict labels of unlabeled instances. Comparative experiments on lots of real-world benchmark datasets are conducted and experimental results show excellent performance of the proposed TS1FRLL compared to the state-of-the-art models of incomplete multi-label learning.